A uniform deformation gradient hexahedron element with artificial hourglass control

An 8-noded linear hexahedron element for large strain hyperelastic analysis is presented in this paper. The element is based on a constant deformation gradient interpolation and is formulated using a mixed variational principle of the Hu-Washizu type. Volumetric and isochoric components of the deformation are treated independently to ensure the correct evaluation of the element volume. A simple procedure to control the propagation of spurious hourglass deformation modes is also discussed. This is based on the addition of artificial hourglass forces which vanish under constant deformation gradient conditions, thereby ensuring that the element passes a non-linear version of the patch test. Applications in the field of neo-Hookean materials and superplastic forming processes are also considered.

[1]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

[2]  R. D. Wood,et al.  Numerical simulation of the superplastic forming of thin sheet components using the finite element method , 1990 .

[3]  Wing Kam Liu,et al.  Use of stabilization matrices in non‐linear analysis , 1985 .

[4]  T. Pian,et al.  On the suppression of zero energy deformation modes , 1983 .

[5]  Global model hourglassing control , 1987 .

[6]  G. A. Frazier,et al.  Treatment of hourglass patterns in low order finite element codes , 1978 .

[7]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .

[8]  J. Oden,et al.  Analysis of hourglass instabilities and control in underintegrated finite element methods , 1984 .

[9]  J. C. Simo,et al.  Quasi-incompressible finite elasticity in principal stretches. Continuum basis and numerical algorithms , 1991 .

[10]  T. Belytschko,et al.  A uniform strain hexahedron and quadrilateral with orthogonal hourglass control , 1981 .

[11]  J. C. Simo,et al.  On the Variational Foundations of Assumed Strain Methods , 1986 .

[12]  J. M. Kennedy,et al.  Hourglass control in linear and nonlinear problems , 1983 .

[13]  John Argyris,et al.  A primer on superplasticity in natural formulation , 1984 .

[14]  L. P. Bindeman,et al.  Assumed strain stabilization of the eight node hexahedral element , 1993 .

[15]  Michael Ortiz,et al.  A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations , 1985 .

[16]  B. C. Noh,et al.  New improved hourglass control for bilinear and trilinear elements in anisotropic linear elasticity , 1987 .

[17]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[18]  Ted Belytschko,et al.  Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems , 1991 .